Find the ratio in which the point P(-1, y) lying on the line segment joining A$(-3,10)$ and B$(6,-8)$ divides it. Also find the value of y.

Let’s P divide A$(-3,10)$ and B$(6,-8)$ in the ratio of k:$1$

Given that the coordinates of P as ($-1$,y)

Now, by using the section formula for x – coordinate we have

$-1=6k–3/k+1$

$-(k+1)=6k–3$

$7k=2$

$k=2/7$

Therefore, the point P divides AB in the ratio of $2:7$

Using value of k, to find the y-coordinate we have

y $=(-8k+10)/(k+1)$

y $=(-8(2/7)+10)/(2/7+1)$

y$=-16+70/2+7=54/9$

y $=6$

Hence, the y-coordinate of P is $6$